Geometric characterization and simulation of planar layered elastomeric fibrous biomaterials

An important class of biomaterials is composed of layered networks of elastomeric fibers. While there is a growing interest in modeling and simulation of the mechanical response of these biomaterials, a theoretical foundation for such simulations has yet to be firmly established. The present work addresses this issue in two ways. First, using methods of geometric probability we develop theoretical estimates for the linear and areal fiber intersection densities for two-dimensional fibrous networks. These are expressed in terms of the fiber density and orientation distribution function, both of which are relatively easy to measure properties. Secondly, we develop a random walk algorithm for geometric simulation of two-dimensional fibrous networks which can accurately reproduce prescribed fiber density and orientation distribution function. Furthermore, the linear and areal fiber intersection densities obtained with the algorithm are in agreement with the theoretical estimates. Both theoretical and computational results are compared with those obtained by post-processing of SEM images of actual scaffolds. These comparisons reveal difficulties inherent to resolving fine details of multilayered fibrous networks. We also note that one should think not in terms of sufficiently large specimens for analysis, but rather sufficiently fiber-filled specimens. Correctly identifying and matching key geometric features is a critically important first step for performing reliable mechanical simulations. The methods provided herein can provide a rational means to define and generate key geometric features from scaffold structural data.